The 'crystal coating' is probably calcite, of a type that forms in open fissures or cavities (including cavities within fossils). I can't quite make out the overall 3D arrangement of the calcite, so I can't comment further at this point.

If you can tell me more about the overall structure, perhaps with the help of more photos, then maybe I could 'see' more in the specimen.

A fault can be a simple surface across which the rocks are dislocated. But it can also be a gaping dislocation, in which case, some of the adjacent rock commonly falls into the cavity. In the latter case, the remaining gaps (between the adjacent rock and the broken lumps) can get filled with precipitated minerals. The mix of lumps of rock and intervening precipitated mineral crystals is called a breccia (breccias can also have ground-up rock in place of the crystals).

In your case, we see the crystal coating going around several sides of the lump. The lump itself seems to have some cracks in it. That suggests to me we are not dealing with part of a simple vein.

My best guess is that the lump is part of a fault breccia, partly cemented by a mineral which may be calcite.

The limestone (or silty limestone, can't tell for sure) is not native to Suffolk; it would have been brought there by man or natural processes.